Internal problem ID [2642]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (\cos ^{2}\relax (y)\right )+\tan \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 35
dsolve(x*cos(y(x))^2+tan(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arccos \left (\frac {1}{\sqrt {-x^{2}-2 c_{1}}}\right ) \\ y \relax (x ) = \pi -\arccos \left (\frac {1}{\sqrt {-x^{2}-2 c_{1}}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.102 (sec). Leaf size: 103
DSolve[x*Cos[y[x]]^2+Tan[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (-\sqrt {-x^2+8 c_1}\right ) \\ y(x)\to \sec ^{-1}\left (-\sqrt {-x^2+8 c_1}\right ) \\ y(x)\to -\sec ^{-1}\left (\sqrt {-x^2+8 c_1}\right ) \\ y(x)\to \sec ^{-1}\left (\sqrt {-x^2+8 c_1}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}